Question

4x4 + 81 find the factors​

Answer 1

Answer:

2,4,6,8,10 are the factors

Step-by-step explanation:

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Answer 2

Answer:

In the given equation 4x

4

+81y

4

, add and subtract 36x

2

y

2

to make it a perfect square as shown below:

4x

4

+81y

4

=(4x

4

+81y

4

+36x

2

y

2

)−36x

2

y

2

=[(2x

2

)

2

+(9y

2

)

2

+2(2x

2

)(9y

2

)]−36x

2

y

2

=(2x

2

+9y

2

)

2

−36x

2

y

2

(using the identity (a+b)

2

=a

2

+b

2

+2ab)

We also know the identity a

2

−b

2

=(a+b)(a−b), therefore,

Using the above identity, the equation (2x

2

+9y

2

)

2

−36x

2

y

2

can be factorised as follows:

(2x

2

+9y

2

)

2

−36x

2

y

2

=(2x

2

+9y

2

)

2

−(6xy)

2

=(2x

2

+9y

2

+6xy)(2x

2

+9y

2

−6xy)

Hence, 4x

4

+81y

4

=(2x

2

+9y

2

+6xy)(2x

2

+9y

2

−6xy)

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